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An  -local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type
Author(s):
Thirupathi
Gudi;
Neela
Nataraj;
Amiya
K.
Pani.
Journal:
Math. Comp.
77
(2008),
731-756.
MSC (2000):
Primary 65N12, 65N15, 65N30
Posted:
November 21, 2007
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Abstract:
In this paper, an  -local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On  -quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in broken  norm and  norm which are optimal in  , suboptimal in  are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results.
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Additional Information:
Thirupathi
Gudi
Affiliation:
Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076
Email:
trpathi@math.iitb.ac.in
Neela
Nataraj
Affiliation:
Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076
Email:
neela@math.iitb.ac.in
Amiya
K.
Pani
Affiliation:
Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076
Email:
akp@math.iitb.ac.in
DOI:
10.1090/S0025-5718-07-02047-9
PII:
S 0025-5718(07)02047-9
Keywords:
$hp$-finite elements,
local discontinuous Galerkin method,
second order quasilinear elliptic problems,
error estimates,
order of convergence
Received by editor(s):
April 14, 2006
Received by editor(s) in revised form:
February 23, 2007
Posted:
November 21, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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